Karhunen-Loève Estimation of the Power Spectrum Parameters from the Angular Distribution of Galaxies in Early Sloan Digital Sky Survey Data

Citation:

Szalay AS, Jain B, Matsubara T, Scranton R, Vogeley MS, Connolly A, Dodelson S, Eisenstein D, Frieman JA, Gunn JE, et al. Karhunen-Loève Estimation of the Power Spectrum Parameters from the Angular Distribution of Galaxies in Early Sloan Digital Sky Survey Data. The Astrophysical Journal. 2003;591 :1-11.

Date Published:

July 1, 2003

Abstract:

We present measurements of parameters of the three-dimensional powerspectrum of galaxy clustering from 222 square degrees of early imagingdata in the Sloan Digital Sky Survey (SDSS). The projected galaxydistribution on the sky is expanded over a set of Karhunen-Loève(KL) eigenfunctions, which optimize the signal-to-noise ratio in ouranalysis. A maximum likelihood analysis is used to estimate parametersthat set the shape and amplitude of the three-dimensional power spectrumof galaxies in the SDSS magnitude-limited sample withr*<21. Our best estimates are Γ=0.188+/-0.04 andσ8L=0.915+/-0.06 (statistical errors only), for a flatuniverse with a cosmological constant. We demonstrate that ourmeasurements contain signal from scales at or beyond the peak of thethree-dimensional power spectrum. We discuss how the results scale withsystematic uncertainties, like the radial selection function. We findthat the central values satisfy the analytically estimated scalingrelation. We have also explored the effects of evolutionary corrections,various truncations of the KL basis, seeing, sample size, and limitingmagnitude. We find that the impact of most of these uncertainties staywithin the 2 σ uncertainties of our fiducial result.

Notes:

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